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How do you determine the mass of a star? The most straightforward way can be done if the star is part of a binary pair. By observing the motion of two stars orbiting each other we can determine both the size of their orbits and their orbital period. From this we can determine the masses of the stars via Kepler’s laws. Binary stars provided the first measure of stellar masses, but many stars are not binary, so we must use alternative methods. 

One of the early ways of estimating the mass of a single star was through observation of its temperature and brightness. The more massive a star, the hotter and brighter it will tend to be. While this works reasonably well for main sequence stars, it isn’t overly accurate. For one thing, stars become hotter as they age, so an older star will seem somewhat more massive than it actually is.

Seismic vibration modes of the Sun. Credit: NASA/Kepler

More recently we’ve been able to use a method known as asteroseismology. It was originally used on the Sun (and then known as helioseismology). Our Sun is not a rigid object, but instead has a more fluid behavior. Solar flares and the convection from its interior create sound waves within the Sun, causing it to oscillate like a ringing bell. These oscillations can be measured by observing the motion of the Sun’s surface using Doppler measurements. Since these oscillations are affected by the density and pressure of the Sun’s interior, we can determine the mass of the Sun (among other things) accurately. We’re now able to make similar measurements of some stars, and can determine their masses in this way.

Sunspots and granules on the Sun’s surface. Credit: NASA Goddard Space Flight Center

Making accurate Doppler measurements of a star is difficult and time consuming. But it turns out we don’t need Doppler measurements to determine a star’s mass. We can simply look at the small fluctuations of a star’s brightness. While the overall brightness of most stars is fairly consistent, stars do experience small fluctuations in their brightness. This can be due to things like starspots, but it is also due to an effect known as granulation. The upper layer of a star undergoes convection, where warmer material rises to the surface pushing cooler material down. As a result, the surface of a star simmers like a pot of oatmeal. Because of this there are always small variations of a star’s brightness, which we can measure as small flickers in stellar brightness.

In a new work, astronomers compared the rate of these flickers to the mass of the star, and found that there was a good correlation between the flicker of a star and its surface gravity. Using data from the Kepler spacecraft, they were able to determine the mass of about 30,000 stars with reasonable accuracy. There are, however, limitations to this method. In particularly it only produces reasonable results for stars with a temperature between 4,500 and 7,000 Kelvin. For stars much cooler or hotter than the Sun the method has limited accuracy. However the ease of this method compared to asteroseismical methods still makes it a useful tool.

Paper: Fabienne A. Bastien, et al. A Granulation “Flicker”-based Measure of Stellar Surface Gravity.  arXiv:1512.03454 [astro-ph.SR]

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NASA’s Solar Dynamics Observatory has been observing the Sun for five years. It’s goal is to study the dynamic variations of the Sun and how they affect our planet. It’s gathered 2.6 petabytes of information, and its data is used for a range of scientific work, from helioseismology and studies of the corona to solar flares and sunspots. It’s also gathered some stunning visuals showing the complex dance of our closest star. Some of the visuals from year five are presented in this wonderful video.

Throughout the video you can see prominences that burst out from the solar surface and wisps of plasma flowing along magnetic field lines. There are filaments looking like cracks in the Sun, and bubbling granules as material from the warmer interior churns toward the Sun’s surface. You can watch coronal mass ejections, and see how the limb of the Sun appears cooler and dimmer. You can even see a transit of Venus.

Often in astronomy, it is the brief moments of fame that get the greatest attention. The landing on a comet, or on Titan. The mission to Ceres, or the upcoming Pluto flyby. These missions deserve the recognition they get, but there are also missions such as the SDO, which quietly gather data, year after year. Though not nearly as sexy, they are just as important as the missions that dance in the Sun.

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The Sun is so intensely bright that it’s difficult to look at (and you shouldn’t try). When observing the Sun with scientific instruments, we often use filters to diminish the light so that we can observe surface features of the Sun in detail, such as sunspots and the churning of granules due to convection near the surface. But how do we study the interior of the Sun?

One way is through neutrinos generated in the Sun’s core. Unlike light, which can take 20,000 to 150,000 years to travel from the Sun’s core to its surface, neutrinos leave the Sun soon after they are produced. We’ve been able to detect solar neutrinos since the 1960s, but these were neutrinos due to secondary reactions in the core. More recently we’ve been able to observe neutrinos from the principle fusion mechanism known as the pp-chain. From these observations we know the rate at which fusion occurs in the Sun, as well as its central pressure, temperature and density.

Between the core and surface things get a bit more tricky. Surrounding the core is a radiative zone, where the heat of the core moves toward the surface mainly through photon radiation. Surrounding that is a convection zone, where stellar material churns in a cycle. Heated by the interior, the material rises toward the surface. It then cools and sinks toward the interior where the process happens all over again. We know of these levels through helioseismology, which is the study of sound waves traveling through the Sun’s interior. While light takes thousands of years to travel from the Sun’s core to its surface, the solar interior is relatively transparent to acoustic waves, which means they can travel through the Sun at the speed of sound.

As the methods of helioseismology have gotten more sophisticated, we’ve been able to determine some of the characteristics of the convection flow, and what we’ve found is that it’s much more turbulent than originally supposed. This means that while our surface and deep interior models are pretty good, our mid-range models aren’t. This isn’t particularly surprising, since the complex transition between the radiative and convective regions is notoriously difficult to model.

But what’s amazing is that we can use sound waves to actually test these models. With methods such as neutrino physics and helioseismology, we can really see the complex beauty of the Sun’s interior.

Paper: Laurent Gizona & Aaron C. Bircha. Helioseismology challenges models of solar convection. PNAS, vol. 109, no. 30, 11896–11897 (2012).

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NASA’s Kepler space telescope has stopped its initial run of collecting data in its search for new planets, but that doesn’t mean there will be no more new discoveries from that data. A good case in point can be seen from a recent article in Nature that demonstrates a clever way to measure the surface gravity of a star.

In order to discover planets, Kepler was pointed at a particular patch of sky and measured the brightness of more than 150,000 stars over long periods of time. When a planet passes in front of a star (from our vantage point), the star will dim measurably. Astronomers have been combing through the Kepler data looking for periodic dips in brightness that indicate a transiting planet. So far we’ve found over 2,700 candidate planets in the data.

Finding evidence of planets from the data is a bit tricky because the data has a lot of variation (called noise) within it. The brightness of a star by itself is not constant. It fluctuates slightly all the time because of things like starspots (sunspots on the star), flares, and even the convective motion of material near the surface of the star, which produces a kind of bubbling porridge effect called granulation.

When searching for planets, all of these fluctuations just get in the way, so you find ways to filter it out to find the planetary signals. But the team behind this article analyzed the noise itself and found it can tell us about the star itself. Since starspots move basically with the rotation of the star, the brightness variations due to the starspots tells us about the rotational speed of the star. The level of granulation is related to the surface gravity of a star, since smaller stars with a higher surface gravity have less granulation than larger stars with a lower surface gravity.

We can analyze this data to determine these properties, but you can get a good idea of how this works by converting the data to sound. In the video above, the brightness variations of the star were sped up and converted to sounds. As a result, the starspot variations sound like low warbles, while the granulation sounds like a static hiss.

These types of observations are useful, because the information we can obtain about a transiting planet is related to the star itself. For example, if we see a star dim by a certain fraction, we know the size of the planet is a certain fraction of the star. But without knowing the size of the star we can’t pin down the planet’s size. So by using the “noise” of the observations to determine the star’s size and mass, we also gain a better measure of the planet’s size and mass.

Since we already have this data from the Kepler mission, we can analyze the noise to further refine our planetary knowledge. Pulling more knowledge from the data we already have.

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Stars like the Sun oscillate due to acoustic waves in their interior.  The study of these sound waves in the Sun is known as helioseismology, and in other stars it’s known as asteroseismology. It turns out to be a very useful tool. While light travels slowly through the star’s interior, taking thousands of years to travel from the its core to its surface, the stellar interior is relatively transparent to acoustic waves, which means they can travel through the star at the speed of sound. Because of this, sound waves in a star can be used to study its interior, similar to the way ultrasound is used to see inside the human body. We do this by measuring the oscillations of a star’s surface using the Doppler shift of spectral lines.

Because the frequency of these acoustic waves depends upon the speed of sound, and the speed of sound depends upon the density and pressure of the star’s interior, we can use asteroseismology to determine the density of the star.  Since the density of a star depends upon its mass and temperature (and we can measure the temperature of a star by its color), asteroseismology can in principle be used to determine the size of a star very precisely.

While we have done helioseismology with the Sun for quite some time, doing asteroseismology with a star is much more difficult.  You need to measure starlight over a long period of time, and you need to analyze it in detail to determine the sound waves.  The good news is that this sort of long term data exists for some stars, such as those observed by the Kepler space telescope.  Now a new paper in the Astrophysical Journal has presents the asteroseismology results of a star known as Kepler-93.

The team used data from Kepler, and through asteroseismology determined its density to be between 1.658 and 1.646  g/cc. They also Its mass to be between 94.4% and 87.8% that of the Sun.  From this, they determined that the radius of the star is 91.9% that of the Sun, give or take 7,600 kilometers.  Basically, they measured the width of this star to within the width of the Earth, which is extraordinarily precise.

Kepler-93 has two known planets. The closer planet (Kepler-93b) transits the star about once every 5 days. From the transit data we can determine the size of the planet relative to the star, so using the transit data and the asteroseismology data the team was able to determine the size of the planet very precisely. They found that it is 1.481 times larger than Earth, give or take 120 kilometers.

Think on this for just a moment. Kepler-93 is 315 light years away, and we know the diameter of the star to within the width of the Earth. We know the diameter of one of its planets to within 120 kilometers. That’s a distance you could travel in a bit more than an hour on an interstate highway. Give or take.

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Determining the age of a star poses a bit of a challenge for astronomers. After all, stars exist over a timescale of billions of years, and they are light years away.  We can’t use radiometric dating like we do for rocks and other objects on Earth.  So just how do we determine the age of a star? It turns out that there are several ways, and it’s getting easier to do.

One of the ways is to compare a star’s mass with its brightness (absolute magnitude).  We can determine the mass of a star if it is part of a binary system, and if we have a good measure of its distance (say, through its parallax) then we can observe its apparent magnitude and use its distance to determine its absolute magnitude.  The way we determine its age is by recognizing that main sequence stars grow hotter and brighter over time.  Stars produce light and heat through nuclear fusion in their core.  As more hydrogen fuses into helium, the fusion rates gradually increase, producing more heat and light.  So for stars of a particular mass, brighter stars are older than dimmer stars.  By observing stars that are newly formed and stars at the end of their life we have an idea of the rate at which stars brighten over time, so we can get a measure of a star’s age.

Another way is to measure a star’s rate of rotation.  For stars around a solar mass or less, the rate of rotation of a star gradually decreases.  So the rotation rate of a star depends upon its mass and age.  By measuring the rotation of a star and comparing it to the rotation of the Sun (for which we know its age very well), we can determine its age.

There are a few downsides with these age measurements.  For one, they only work with main sequence stars, so very young and very old stars need to be studied with different measures.  For another, they depend upon measurements that have traditionally been challenging to do well.  But a new method presented in the Astrophysical Journal could provide an easier and more effective way to determine stellar ages.

The method uses what is known as helioseismology, which is the study of sonic oscillations within a star.  Helioseismology has long been used to study the interior structure of the Sun, but more recently it can also be used with stars.  Since the frequency of sound oscillations depends upon the mass and density of a star, helioseismology can be used to determine the mass and radius of a star pretty effectively.  Knowing that, one can use observations of a star’s spectrum to determine its temperature.  The mass, radius and temperature of a star can then be used to determine its age.

What makes this new method potentially powerful is that it depends upon the type of observational data gathered by sky surveys.  This initial study looked at about a thousand stars.  A larger project known as the Stroemgren survey for Asteroseismology and Galactic Archaeology (SAGA) is analyzing data gathered by the Kepler telescope.  Future observations by telescopes such as GAIA could provide a large survey of stellar ages within our galaxy.

The reason why this is important is that knowing the age of a large number of stars allows us to study the history of our galaxy.  By analyzing stellar ages, we can determine when star production was common, and when it was rare.  We might even be able to determine past collisions with our galaxy, which tend to drive star production.  This new method is still young, so it will take time to determine if it lives up to its potential.  But if it does we may soon gain deeper understanding of the history of our galaxy.

Paper: L. Casagrande, et al. Stroemgren survey for Asteroseismology and Galactic Archaeology: let the SAGA begin.  L. Casagrande, et al. arXiv:1403.2754 (2014)

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There’s a song of the Sun.  It is produced by acoustic waves in the Sun’s interior, and the study of these waves is known as helioseismology.  It turns out to be a very useful tool.  While light travels slowly through the Sun’s interior, taking thousands of years to travel from the Sun’s core to its surface, the solar interior is relatively transparent to acoustic waves, which means they can travel through the Sun at the speed of sound.

A computer plot of one oscillation mode of the Sun. Credit: NOAO

Because of this, sound waves in the Sun can be used to study the Sun’s interior, similar to the way ultrasound is used to see inside the human body.  The difference is that we can’t send sound waves through the Sun, but instead have to measure the natural sound waves that occur within the Sun.  We do this by measuring the oscillations of the Sun’s surface using the Doppler shift of spectral lines.

By analyzing these oscillations, we know that the interior of the Sun (known as the radiation zone because heat transfers radiantly in the core) rotates uniformly, while the outer layers (the convection zone) rotate differentially by latitude.  Acoustic analysis also gives us a measure of how the density and pressure of the Sun varies by depth, since the speed of sound within the Sun is affected by density and pressure.

There are even audio recordings of the Sun, where the solar oscillations have been speed up a bit and converted to sounds we can hear.  You can hear several of them here.

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